Yes it is possible to do an unattended installation using a kickstart file that is located on a supported location:
USB Flash Drive
Network location using a supported protocol (e.g.: HTTP, FTP)
Refer to these pages for more details (I recommend that you read the whole section titled "Installing or Upgrading Hosts by Using a Script"):
You can automate the installation of esxi with "kickstart" configuration file.
This file will include the the configuration setting like hostname, Ip address, datastore, subnet mask, license keys
The kickstart configuration file can be placed in either of the places:
Locally attached storage (local)
Network storage (remote)
USB disks (usb)
HTTP, HTTPS, FTP, NFS, CDROM, or USB.
You can also boot boot it from a CD/DVD or USB drive